The invention generally concerns the linear Minimum Mean Squared Error (MMSE) criterion, which minimizes the Mean Squared Error (MSE) between the receiver output and the desired data for communication receiver design. Exemplary applications that the invention is applicable to include equalization, crosstalk cancellation, beamforming using antenna arrays, and multiuser detection in Code Division Multiple Access (CDMA) systems.
The invention provides communication receiver crosstalk suppression. Additional applications of the invention include equalization for single user differentially modulated systems.
A basic problem in wired and wireless communications concerns an interference which can cause a receiver to decode something other than the data which was sent to it. Interference may be suppressed or compensated to limit such errors. As an example, single user communication over a dispersive channel is limited by the presence of intersymbol interference (ISI). For multiuser communication, an additional impairment is due to multiple-access interference (MAI). Methods for mitigating ISI are referred to as equalization, and methods for mitigating MAI are referred to as multiuser detection or interference suppression. The linear minimum mean squared error MMSE criterion has been used to design equalizers for decades. Recently, it was recognized that it could also be used to design receivers for interference suppression for direct sequence CDMA systems with short spreading sequences, in which the MAI has a repetitive structure that can learned and exploited by the receiver. The key advantage of the MMSE criterion is that it yields adaptive receiver training algorithms. Such algorithms typically use an initial training sequence of known data, followed by continued decision-directed adaptation based on receiver decisions. The requirement of known data for training is, however, also a drawback since it uses otherwise available bandwidth.
With the recent growth in wireless communications, there is much interest in applying equalization/interference suppression to wireless channels. However, a major impairment in a wireless communication system is fading, which causes severe fluctuations in the amplitude and phase of the received signal. Fading is caused by varied distances from a transmitter, atmospheric conditions, and other phenomena which causes such fluctuations. Known existing adaptive algorithms cannot track these fluctuations even for moderate levels of fading, without a large overhead in terms of known pilot symbols. The known algorithms therefore have little practical value since pilot symbols exhaust excessive bandwidth.
Known techniques also have shortcomings in beamforming applications for receive antenna arrays. For direct sequence CDMA systems with long spreading sequences, the MAI does not have a repetitive structure in the time domain, so that time domain adaptive algorithms do not apply. However, if the receiver is equipped with an antenna array, the MAI has a repetitive structure in the spatial domain, because the array response to the signal arriving from a given user varies slowly over time. The problem is how to exploit this feature to adaptively put nulls in the directions of the MAI. The known methods fail because of the required sequence of training symbols to be transmitted by the user of interest. The complexity of the known algorithms are a further drawback.
Some prior methods have sought to address these problems. For single user applications, one method for dealing with fading channels is to insert known pilot symbols periodically, and use these to track the amplitude and phase of the desired user. The overhead required for this can be quite high, especially for channels that vary fast (so that pilot symbols must be inserted more frequently). This method has also been proposed for multiuser applications in H. V. Poor and X. Wang, xe2x80x9cAdaptive Multiuser Detection in Fading Channelsxe2x80x9d, Proc. 34th Annual Allerton Conf. on Communications, Computing and Control, Monticello, Ill., October.
Another prior method for dealing with fading channels is to use blind algorithms that do not attempt to track amplitude and phase fluctuations, but exploit some other known feature of the desired user (e.g., knowledge of spreading waveform and timing of desired user for interference suppression, see, M. Honig, U. Madhow, S. Verdu, xe2x80x9cBlind Adaptive Multiuser Detectionxe2x80x9d, IEEE Transactions on Information Theory, Vol. 41, No. 4, July 1995, or knowledge of array response for desired user in beamforming, see, D. H. Johnson, D. E. Dudgeon, Array Signal Processing: Concepts and Techniques, Englewood Cliffs, N.J., Prentice-Hall, 1993). Such methods will fail to produce the desired signal suppression if the knowledge regarding the desired signal is inaccurate. In addition, they have poorer performance in terms of convergence and steady state performance than training based methods.
The use of differential modulation to avoid tracking amplitude and phase for CDMA systems with fading was proposed in M. Honig and M. Shensa and S. Miller and L. Milstein, xe2x80x9cPerformance of Adaptive Linear Interference Suppression for DS-CDMA in the Presence of Flat Rayleigh Fadingxe2x80x9d, Proc. of VTC""97, 1997. An adaptive algorithm for receiver training was proposed. However, this algorithm is not robust, and periodically needs to switch to a fallback mode in which the blind algorithm of M. Honig, U. Madhow and S. Verdu, xe2x80x9cBlind Adaptive Multiuser Detectionxe2x80x9d, IEEE Transactions on Information Theory, Vol. 41, No. 4, July 1995, is used. Two of the inventors on the present invention suggested a fix to this problem in L. J. Zhu, U. Madhow, xe2x80x9cAdaptive Interference Suppression for Direct Sequence CDMA over Severely Time-Varying Channelsxe2x80x9d, Proc. IEEE Gloecom ""97, where the correlator updates from a standard LMS or RLS algorithm were scaled to maintain approximately unit energy at the correlator output. The latter approach was an ad hoc fix, however, and failed to provide a systematic framework for algorithm development and extensions which are fundamental to design of practical communication systems.
General blind source separation algorithms also exist for separating a number of independent users using antenna arrays, see, for example, X. Cao and R. Liu, xe2x80x9cGeneral Approach to Blind Source Separationxe2x80x9d, IEEE Transactions on Signal Processing, Vol. 44, No. 3, pp. 562-71. However, these algorithms are complex, and their performance is not as good as that of algorithms that exploit application-specific features. Better algorithms that do exploit the properties of CDMA with long spreading sequences have been proposed in the literature. See, e.g. H. Liu, M. D. Zoltowski, xe2x80x9cBlind Equalization in Antenna Array CDMA Systemsxe2x80x9d, IEEE Trans. Signal Proc., Vol. 25, No. 1, pp. 161-172, Jan. 1997, and A. Naguib, xe2x80x9cAdaptive Antennas for CDMA Wireless Networksxe2x80x9d, Ph.D. Dissertation, Stanford University, August 1996. While these address some problems, alternatives to these are desirable.
This invention reformulates the MMSE criterion so that it applies to systems in which the desired data to track is the ratio of the data appearing in successive observation intervals. The resulting differential MMSE criterion leads to a number of novel algorithms for adaptive implementation of the MMSE receiver. Applications include equalization for single user systems and multiuser detection, or interference suppression, for direct sequence CDMA systems employing short spreading sequences (i.e., the period of the spreading sequence equals the symbol interval). The invention also provides a method for blind, i.e., without knowledge of the symbol sequence sent by the user of interest, equalization or beamforming (using a receive antenna array) for direct sequence CDMA systems with long spreading sequences, i.e., systems in which the spreading sequences are aperiodic, or have period much larger than the symbol interval. Equalization and interference suppression for direct sequence CDMA with short spreading sequences is provided by the invention to enable interference suppression without tracking the fading channel seen by the desired user. The invention therefore enables recovery of the desired symbol sequence up to an unknown phase. Hence, the invention is well suited to the demodulation of differentially modulated data in which information is encoded in the phase differences of successive transmitted symbols. Assuming that the amplitude and phase over a fading channel is approximately constant over two successive symbol intervals, the demodulator can use the differences in phases of two successive received symbols to recover differentially encoded data. It is also possible to use the invention in conjunction with a separate phase recovery method to demodulate data without differential modulation.
The invention may be used to conduct blind equalization and beamforming for direct sequence CDMA systems with long spreading sequences based on the observation that the unknown symbols of the desired user are constant over the elements (referred to herein as xe2x80x9cchipsxe2x80x9d) of the spreading sequence within the symbol interval. Since the spreading sequence of the desired user is known, the ratio of two successive chips within a symbol interval is known. Therefore, the following analogy may be established with a CDMA system with short spreading sequences: (a) the unknown symbol modulation plays the role of slow fading that the invention avoids tracking, (b) the known spreading sequence for the desired user plays the role of a training sequence at the chip rate, (c) the array response plays the role of a short spreading sequence.